Consider that you need to determine how to power a load that will double after 3...

Consider that you need to determine how to power a load that will double after 3 years of the initial operation. You have the option of buying enough DG units to power the initial load and the load increase in 3 years for $ 2M or you can buy enough for the initial load by $1M and buy the rest of the DG units in 3years. Consider that the annual inflation rate is 3%. You are financing your capital investment with a loan. Loans interest rate are a couple of points above a savings account interest rate which, in turn, is a couple of points above the inflation rate. Thus, the savings account rate is 5% and the loan’s rate is 7%. What should you do? You have 3 options, please solve all the three of them: A.Get a loan today for $2M for all the present capacity plus the load increase in year 3. B.Get a loan for $1M now to power the initial load and after 3 years an additional loan for $1M. C.Get a loan today for $2M, use only what it is needed initially ($1M) and invest the rest until using it in year 3

Solutions

Expert Solution

Option a)

Get $2million loan @ 7% for 3years. (Assume annually compounded)

Value of the loan after 3 years = Loan amount*[(1+interest rate)^3years] = $2million*[(1+0.07)^3] = $2million*(1.07^3) = $2million*1.225043 = $2,450,086

Option b)

Get $1million loan @ 7% for 3years. (Assume annually compounded)

Value of the loan after 3 years = Loan amount*[(1+interest rate)^3years] = $1million*[(1+0.07)^3] = $1million*(1.07^3) = $1million*1.225043 = $1,225,043

Value of DG units after 3 years = Present value*[(1+Inflation rate)^3years] = $1million*[(1+0.03)^3] = $1million*(1.03^3) = $1million*1.092727 = $1,092,727

Loan to be obtained after 3 years for DG units = Value of DG units after 3 years = $1,092,727

Total value of loan after 3 years = $1,225,043+$1,092,727 = $2,317,770

Option c)

Get $2million loan @ 7% for 3years. (Assume annually compounded)

Deposit of 1million @ 5% for 3years

Maturity value of deposit after 3 years = Deposit amount*[(1+saving interest rate)^3years] = $1million*[(1+0.05)^3] = $1million*(1.05^3) = $1million*1.157625 = $1,157,625

Value of DG units after 3 years = Present value*[(1+Inflation rate)^3years] = $1million*[(1+0.03)^3] = $1million*(1.03^3) = $1million*1.092727 = $1,092,727

Excess of deposit available after DG purchase = Maturity value of deposit after 3 years - Value of DG units after 3 years = $1,157,625 - $1,092,727 = $64,898

Value of the loan after 3 years = Loan amount*[(1+interest rate)^3years] - Excess deposit available = $2million*[(1+0.07)^3] - $64,898 = $2million*(1.07^3) - $64,898 = ($2million*1.225043) - $64,898 = $2,450,086 - $64,898 = $2,385,188

Since considering all the options outflow, option 2 is better because it has least outflow.

jeff jeffy answered 1 year ago

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